پاسخ دینامیکی بستر خاکی زیر ریل های دوتایی راه آهن سریع السیر Dynamic responses of subgrade under double-line high-speed railway

1. Introduction Nowadays, there is a great interest in the construction of high-speed railways worldwide, and high-speed railways have been built to connect major cities in countries in Asia and Europe, making travelling easier for passengers. While high-speed trains enable passengers to arrive at their destination faster, the high speeds also lead to several problems in the sub-systems of high-speed railways, which will threaten passenger safety. This is indeed evident from the statistics of accidents that occur on high-speed railways. In 1998, the Inter City Express (ICE) derailed near the village of Eschede, Germany, due to fatigue fracture of the double hub wheel of the high-speed train under dynamic loads. In 2000, two pairs of wheels of a Eurostar high-speed train travelling at full speed (300 km/h) derailed because of the uneven subgrade, resulting in 14 casualties. In 2004, a brand-new high-speed train was overthrown in Turkey as a result of derailment, which is likely because the old rail was not suitable for the new high-speed train. In 2013 and 2015, an AVE Talgo high-speed train and a TGV high-speed test train derailed as the trains sped around the corner. All of these train accidents indicate that it is crucial to investigate the performance of high-speed railway systems (i.e. train, track, and subgrade) under dynamic loads. At present, the main models of high-speed trains comprise the Shinkansen series (Japan), TGV series (France), Eurostar series (United Kingdom), ICE series (Germany), AVE series (Spain), and CRH series (China) with axle loads ranging from 11.3 to 20 t. There are two types of track structure: (1) ballasted track and (2) ballastless track. Ballastless tracks provide smoother, comfortable ride, superior durability, and lower maintenance compared with conventional ballasted tracks. Therefore, ballastless tracks are typically used for high-speed railways with train speeds of 250 km/h and above. Subgrade is the subsystem of high-speed railways with a relatively small stiffness and it serves as the foundation for the train and track structure. The stress distributions of the subgrade structure subject to dynamic loads (particularly, high-speed dynamic loads) are intrinsically complex. The safety of high-speed railway systems will be greatly affected if the dynamic responses of the subgrade structure exceed permissible limits. Studies on the dynamic responses of subgrade structures can be divided into three categories: (1) theoretical studies, (2) experimental studies, and (3) numerical simulations. Theoretical studies are focused on the development of different subgrade models using analytical methods. In earlier theoretical studies, the entire subgrade structure was treated as an elastic half-space body. Jones et al. [1] used the dynamic stiffness matrix method to investigate the attenuation of ground vibrations, where the ground was modelled as an elastic half-space body. Krylov [2] adopted the Green function method to study the effect of train speed on the ground dynamic response. Dieterman et al. [3] determined the equivalent stiffness of an elastic half-space body (sub-soil) using Fourier transform in the spatial and temporal domains and the results showed that the critical velocity results in resonance. Grundmann et al. [4] defined the sub-soil as a layered half-space body and analysed its dynamic response using the wavelet transformation method.